Superrationality: How Decision Theory Resolves Any Dilemma

Chapter III: Why Eve is wrong

This is a follow-up to Chapter I and Chapter II.

Remember Eve? She decided to one-box in Newcomb’s problem (Omega’s game with the two boxes), because everyone who one-boxed got $1,000,000 (whereas everybody who two-boxes got only $1,000).

This is a reasonable approach to decision making, but one that is ultimately flawed. This chapter aims to show why Eve is wrong in her reasoning. But first: what is evidence, really?

How evidence works

Imagine a hypothetical world in which 5 in 100 people (5%) have COVID-19. In this world, there is a device for detecting the disease.

This device has the following statistics: if 1000 people infected with COVID-19 get tested with the device, 900 will test positive (90%). If however a 1000 healthy people get tested, 100 (10%) will still get a positive test (even though they don’t have COVID-19).

A woman gets tested positively. What is the probability she has COVID-19?

Intuitively, you might think this probability is somewhere around 0.9 (or 90%) — because 900 out of 1000 people with COVID-19 get tested positively — but you have to remember only 5 in 100 people even have the disease.

So let’s take a group of 2000 people from our hypothetical world, who are all tested with our device. If this group is representative…